FIG. 5 shows the basic elements of an end-to-end transmission within the Public Switched Telephone Network (hereinafter “PSTN”). The PSTN shown includes first and second Users, first and second Central Offices, and a Switched Digital Network. An Analog Subscriber Loop connects the Users to their respective Central Offices, and the Switched Digital Network connects the Central Offices together. The Analog Subscriber Loops are conventional twisted pairs that transport analog signals from the User Equipment to the associated local Central Office. At the Central Office, the analog signals are converted to 64 kbps DS0 digital data streams by a channel unit filter and codec, which together implement a bandlimiting filter followed by a nonlinear encoding rule and subsequent analog to digital conversion. The resulting DS0 streams are transported to their respective destination Central Office via the Switched Digital Network.
At the Central Office 1, User's 1 loop signal is first bandlimited. The bandlimited analog signal is then sampled at a rate of 8 ksamples/second, and then converted into an 8-bit digital representation using a nonlinear mapping rule referred to as PCM encoding. This encoding is approximately logarithmic, and its purpose is to permit relatively large dynamic range voice signals to be represented with only 8 bits per sample.
Users 1 and 2 may use a conventional modem, as shown in FIG. 6, to transmit digital data over the configuration of FIG. 5. The conventional modem encodes the user's digital data into a symbol sequence. The symbol sequence is then represented as an appropriately bandlimited analog signal which can be transmitted over the approximately 3.5 kHz bandwidth available on the end-to-end connection. The exemplary modem of FIG. 6 includes a Digital to Analog converter (i.e. D/A),) an Analog to Digital converter (i.e. A/D), and a hybrid. The A/D and the D/A perform PCM encoding. The non-linearity associated with the PCM coding is incorporated in the circuitry that converts the analog signals to digital signals, and vice-versa. That is, the analog voltage level of the received signal is mapped to the nearest PCM quantization level, and vice versa, so that the PCM quantization levels serve as the channel symbol alphabet.
PCM baseband modulation in the upstream direction, i.e. from User 1 to the Central Office, presents special equalization problems. For instance, one potential application for PCM baseband modulation in the upstream direction is in conjunction with “56k” modems. However, “56k” modems have a zero in the frequency band of interest. The zero at zero frequency comes from the transformer coupling of the analog subscriber loop to the central office equipment. Therefore, telephone lines do not pass DC signals. Low frequencies near DC are also attenuated significantly as to rule out linear equalization of this channel. Moreover, it is not possible to avoid the zero at DC for 56k modems using pass-band modulation as in the case of earlier V.34 modems because the central site modem is limited to using the sampling rate and quantization levels of the PCM codec at the central office.
One possible way to equalize this channel is to use a linear equalizer to reduce the channel response to a simpler “partial” response that still possesses the zero in the channel but can be dealt with using a non-linear technique such as maximum likelihood sequence (MLSE) decoding or decision feedback equalization (DFE). This however is only possible in the direction of digital modem to analog modem, also referred as the downstream direction. The reason this approach or any linear equalization scheme does not work in the upstream direction is that only PCM codec levels themselves can pass through the PCM codec unscathed. Any filtered version of a sequence of PCM levels will be a linear combination of these levels and in general not be a PCM level itself. When such intermediate levels are quantized by the PCM codec, quantization noise is introduced into the signal erasing any advantage over V.34 techniques.
Accordingly, there exists a need for a system capable of equalizing transmissions from an analog modem.